The analysis and improvement of focused source reproduction with wave field synthesis

This thesis presents a treatise on the rendering of focused sources using wave field synthesis (WFS). The thesis describes the fundamental theory of WFS and presents a thorough derivation of focused source driving functions including, monopoles, dipoles and pistonic sources. The principle characteristics of focused sources including, array truncation, spatial aliasing, pre-echo artefacts, colouration and amplitude errors are analysed in depth and a new spatial aliasing criterion is presented for focused sources. Additionally a new secondary source selection protocol is presented allowing for directed and symmetrically rendered sources. This thesis also describes how the low frequency rendering of focused sources is limited by the focusing ability of the loudspeaker array and thus derives a formula to predict the focusing limits and the corresponding focal shift that occurs at low frequencies and with short arrays. Subsequently a frequency dependent position correction is derived which increases the positional accuracy of the source. Other characteristics and issues with the rendering of focused sources are also described including the use of large arrays, rendering of moving focused sources, issues with multiple focused sources in the scene, the phase response, and the focal point size of focused sound field. The perceptual characteristics are also covered, with a review of the literature and a series of subjective tests into the localisation of focused sources. It is shown that an improvement in the localisation can be achieved by including the virtual first order images as point sources into the WFS rendering. Practical rendering of focused sources is generally done in compromised scenarios such as in non-anechoic, reverberant rooms which contain various scattering objects. These issues are also covered in this thesis with the aid of finite difference time domain models which allow the characterisation of room effects on the reproduced field, it is shown that room effects can actually even out spatial aliasing artefacts and therefore reduce the perception of colouration. Scattering objects can also be included in the model, thus the effects of scattering are also shown and a method of correcting for the scattering is suggested. Also covered is the rendering of focused sources using elevated arrays which can introduce position errors in the rendering.